X₂₃₂₁

X₂-ISOCONJUGATE OF X₁₄₀₈

X₂₃₂₁ = isogonal conjugate of X₁₄₁₂

5, 6, 7 3, 4, 5 Kepler Kimberling

X₂₃₂₁ (X₂-ISOCONJUGATE OF X₁₄₀₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {8, 9}, {10, 37}

• Related Centers: X₁₄₁₂ (-BETH CONJUGATE OF X₈₁), X₈ (NAGEL POINT), X₉ (MITTENPUNKT), X₁₀ (SPIEKER CENTER), X₃₇ (CROSSPOINT OF INCENTER AND CENTROID)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₁₄₀₈

Barycentrics: \(Barycentrics (b + c) (a - b - c) : :\)

Search Value (6, 9, 13): \(4.854219309210\)

▸ Alternate Coordinates1 form

• Trilinears: tan( angle B_AAC_A) : :, where B_A and C_A are the touchpoints of the B- and C-excircles with line BC, resp.

▸ Incident Central Lines19 lines

{1, 2345}, {6, 519}, {8, 9}, {10, 37}, {33, 200}, {69, 527}, {71, 1018}, {72, 1903}, {75, 142}, {141, 536}, {145, 1449}, {190, 319}, {226, 306}, {284, 1043}, {314, 646}, {515, 1766}, {644, 2287}, {1089, 1826}, {1266, 1278}

▸ Functional Relations12 relations

• X₂₃₂₁ = isogonal conjugate of X₁₄₁₂

• X₂₃₂₁ = isotomic conjugate of X₁₄₃₄

• X₂₃₂₁ = complement of X₃₈₇₅

• X₂₃₂₁ = anticomplement of X₃₉₄₆

• X₂₃₂₁ = anticomplementary conjugate of anticomplement of X₃₈₈₂₅

• X₂₃₂₁ = X_i-Ceva conjugate of X_j for (i,j )= (8,210), (321,10), (646,522)

• X₂₃₂₁ = cevapoint of X₁₃₃₄ and X₂₃₁₈

• X₂₃₂₁ = X₂₁₀-cross conjugate of X₁₀

• X₂₃₂₁ = cevapoint of X₁₃₃₄ and X₂₃₁₈

• X₂₃₂₁ = crosssum of X_i and X_j for these (i,j): (56, 604), (1333, 1408)

• X₂₃₂₁ = excentral-to-ABC barycentric image of X₆

• X₂₃₂₁ = barycentric product X₈*X₁₀